I wonder if you have ended up with two DHCP servers; your Router/Modem and XP Pro.
So the first thing to resolve is, are you using static addresses? If so make sure the Router is set to recognise them.
If your using "auto-addressing", make sure the Router is the DHCP server and both your computers are set to obtain their addresses from the router.
Just a thought.
The other thing I would check, is have a command line window open on the problem machine and as soon as you loose the connection, try pinging the router and see what response you get. If the ping answers as normal, then has that reset the connection or do you still have a problem? If you still have a problem, does the "Release all / Renew all" commands get you back up and running?
I'm sure you know, it's a question of trying to pin-point where the problem lays.